Below are listed rank-two temperaments supported by the 37edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments with badness below 0.1

Listed is the wedgie and the TE badness times 1000 for two temperaments with badness less than 0.1.

1	<<3 5 1]]	Porcupine	30.778	250/243
2	<<8 1 -17]]	Würschmidt	40.603	393216/390625

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for four temperaments with badness less than 0.06.

Rank	Wedgie	Name	Badness	Commas
1	<<16 2 5 -34 -37 6]]	Hemiwürschmidt	20.307	2401/2400 3136/3125
2	<<3 5 -6 1 -18 -28]]	Porcupine	41.057	64/63 250/243
3	<<2 -9 -4 -19 -12 16]]	Beatles	45.872	64/63 686/675
4	<<78 19 29 -151 -173 14]]		56.890	2401/2400 133590662774784/133514404296875

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for nine temperaments with badness less than 0.05.

Rank	Wedgie	Name	Badness	Commas
1	<<3 5 -6 4 1 -18 -4 -28 -8 32]]	Porcupine	21.562	55/54 64/63 100/99
2	<<16 2 5 9 -34 -37 -41 6 14 8]]	Hemiwur	29.270	121/120 176/175 1375/1372
3	<<30 13 14 3 -49 -62 -99 -4 -38 -40]]	Cotritone	32.225	385/384 1375/1372 4000/3993
4	<<13 -3 11 5 -35 -19 -37 34 22 -24]]	Twothirdtonic	40.768	121/120 176/175 686/675
5	<<5 -4 -10 -18 -18 -30 -46 -12 -28 -16]]	Passion	40.809	64/63 100/99 1375/1372
6	<<94 21 34 2 -185 -210 -322 20 -68 -112]]		43.106	2401/2400 43923/43904 172032/171875
7	<<14 11 9 -6 -15 -25 -58 -10 -52 -48]]	Quasitemp	43.209	100/99 385/384 1375/1372
8	<<2 -9 -4 -22 -19 -12 -42 16 -20 -48]]	Beatles	45.639	64/63 100/99 686/675
9	<<9 15 19 12 3 5 -12 2 -24 -32]]	Ammonite	45.694	55/54 100/99 686/675

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 22 temperaments with badness less than 0.04.

Rank

Wedgie

Name

Badness

Commas

1	[3 5 -6 4 17 1 -18 -4 16 -28 -8 21 32 70 44]	Porcupinefish	25.314	55/54 64/63 91/90 100/99
2	[13 -3 11 5 12 -35 -19 -37 -29 34 22 39 -24 -7 23]	Twothirdtonic	25.941	91/90 121/120 169/168 176/175
3	[94 21 34 2 27 -185 -210 -322 -305 20 -68 -15 -112 -50 86]		26.829	1001/1000 1716/1715 4225/4224 6656/6655
4	[9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]	Ammonite	27.168	55/54 91/90 100/99 169/168
5	[46 15 19 12 14 -83 -99 -140 -148 2 -24 -23 -32 -31 4]		27.429	385/384 625/624 847/845 1375/1372
6	[16 2 5 9 -8 -34 -37 -41 -72 6 14 -26 8 -41 -61]	Hemiwur	28.432	121/120 176/175 196/195 275/273
7	[30 13 14 3 22 -49 -62 -99 -76 -4 -38 3 -40 10 65]	Cotritone	28.683	169/168 364/363 1001/1000 1716/1715
8	[27 8 20 -1 5 -50 -44 -95 -92 24 -30 -18 -72 -60 21]	Emka	29.741	196/195 364/363 385/384 625/624
9	[2 -9 -4 -22 -1 -19 -12 -42 -9 16 -20 31 -48 12 78]	Beatles	30.161	64/63 91/90 100/99 169/168
10	[5 -4 -10 -18 -21 -18 -30 -46 -52 -12 -28 -34 -16 -22 -6]	Passion	30.886	64/63 100/99 196/195 275/273
11	[18 -7 1 -13 -9 -53 -49 -83 -81 22 -6 5 -40 -29 17]		32.205	176/175 196/195 364/363 512/507
12	[19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]	Semaja	32.564	121/120 169/168 176/175 275/273
13	[14 11 9 -6 -7 -15 -25 -58 -63 -10 -52 -57 -48 -53 -2]		32.913	100/99 196/195 275/273 385/384
14	[11 6 15 27 13 -16 -7 5 -20 18 42 8 24 -19 -55]		33.562	55/54 91/90 169/168 176/175
15	[2 -9 -4 15 -1 -19 -12 17 -9 16 66 31 56 12 -59]		33.971	55/54 64/63 91/90 169/168
16	[11 6 15 -10 13 -16 -7 -54 -20 18 -44 8 -80 -19 82]		34.295	91/90 100/99 169/168 385/384
17	[3 5 -6 4 -20 1 -18 -4 -43 -28 -8 -65 32 -34 -84]		35.130	55/54 64/63 100/99 196/195
18	[48 6 15 -10 13 -102 -111 -182 -157 18 -44 8 -80-19 82]		35.398	364/363 1001/1000 1716/1715 3136/3125
19	[17 16 3 -2 10 -14 -43 -62 -47 -38 -60 -36 -16 17 42]		35.724	100/99 169/168 275/273 385/384
20	[21 -2 -5 -9 8 -52 -67 -87 -65 -6 -14 26 -8 41 61]		37.577	169/168 176/175 364/363 640/637
21	[8 1 -16 -14 -4 -17 -48 -50 -36 -40 -36 -13 16 48 38]		37.834	64/63 100/99 169/168 275/273
22	[35 9 4 -15 1 -67 -92 -145 -128 -16 -66 -31 -56 -12 59]		39.533	364/363 625/624 1375/1372 2200/2197